Properties

Label 722.6.c
Level $722$
Weight $6$
Character orbit 722.c
Rep. character $\chi_{722}(429,\cdot)$
Character field $\Q(\zeta_{3})$
Dimension $286$
Sturm bound $570$

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Defining parameters

Level: \( N \) \(=\) \( 722 = 2 \cdot 19^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 722.c (of order \(3\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 19 \)
Character field: \(\Q(\zeta_{3})\)
Sturm bound: \(570\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(722, [\chi])\).

Total New Old
Modular forms 990 286 704
Cusp forms 910 286 624
Eisenstein series 80 0 80

Trace form

\( 286 q + 4 q^{2} + 29 q^{3} - 2288 q^{4} + 44 q^{5} - 4 q^{6} + 784 q^{7} - 128 q^{8} - 11896 q^{9} + O(q^{10}) \) \( 286 q + 4 q^{2} + 29 q^{3} - 2288 q^{4} + 44 q^{5} - 4 q^{6} + 784 q^{7} - 128 q^{8} - 11896 q^{9} + 200 q^{10} + 1110 q^{11} - 928 q^{12} + 1410 q^{13} + 1400 q^{14} - 934 q^{15} - 36608 q^{16} + 860 q^{17} + 4528 q^{18} - 1408 q^{20} - 5046 q^{21} + 2164 q^{22} + 1734 q^{23} - 64 q^{24} - 86183 q^{25} + 496 q^{26} - 29806 q^{27} - 6272 q^{28} + 4226 q^{29} - 7792 q^{30} + 1928 q^{31} + 1024 q^{32} + 12061 q^{33} - 6088 q^{34} + 12704 q^{35} - 190336 q^{36} + 5448 q^{37} - 94464 q^{39} + 3200 q^{40} + 23031 q^{41} + 26368 q^{42} + 18202 q^{43} - 8880 q^{44} + 45028 q^{45} + 15712 q^{46} + 42798 q^{47} + 7424 q^{48} + 733762 q^{49} + 8232 q^{50} + 50474 q^{51} + 22560 q^{52} - 42498 q^{53} - 27124 q^{54} - 71698 q^{55} - 44800 q^{56} - 79056 q^{58} + 84331 q^{59} - 14944 q^{60} + 24876 q^{61} - 5440 q^{62} - 144568 q^{63} + 1171456 q^{64} + 153536 q^{65} + 71052 q^{66} - 42791 q^{67} - 27520 q^{68} - 175664 q^{69} - 3216 q^{70} + 47514 q^{71} - 36224 q^{72} - 61317 q^{73} - 125672 q^{74} - 372870 q^{75} - 489876 q^{77} + 13352 q^{78} - 25988 q^{79} + 11264 q^{80} - 864131 q^{81} - 95788 q^{82} + 172622 q^{83} + 161472 q^{84} + 44932 q^{85} - 36496 q^{86} + 367080 q^{87} - 69248 q^{88} + 304090 q^{89} + 331936 q^{90} - 445300 q^{91} + 27744 q^{92} - 544952 q^{93} - 425552 q^{94} + 2048 q^{96} + 379003 q^{97} + 6628 q^{98} + 45692 q^{99} + O(q^{100}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(722, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{6}^{\mathrm{old}}(722, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(722, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(38, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(361, [\chi])\)\(^{\oplus 2}\)